Analysis of an eddy current and micromagnetic model

References

• Alouges , F and Soyeur , A . 1992 . On global weak solutions for Landau--Lifshitz equations: existence and nonuniqueness, . Nonlinear Analysis, Theory, Methods and Applications , 18 ( 11 ) : 1071 – 1094 .
   Web of Science ®Google Scholar
• Chen , Y . 1996 . A remark on the regularity for Landau-Lifshitz Equations. . Applicable Analysis , 63 : 201 – 221 .
   Google Scholar
• Chen , Y . 2002 . Existence and singularities for the Dirichlet boundary value problems of Landau-Lifshitz equations. . Nonlinear Analysis , 48A ( 3 ) : 411 – 426 .
   Google Scholar
• Chen , Y and Guo , B . 1996 . Two dimensional Landau-Lifshitz equation. . Journal of Partial Differential Equations , 9 : 313 – 322 .
   Google Scholar
• Cimrák , I . 2005 . Error estimates for a semi-implicit numerical scheme solving the Landau-Lifshitz equation with an exchange field. . IMA Journal of Numerical Analysis , 25 : 611 – 634 .
   Google Scholar
• Cimrák , I and Slodička , M . 2004 . An iterative approximation scheme for the Landau-Lifshitz-Gilbert equation. . Journal of Computational and Applied Mathematics , 169 : 17 – 32 .
   Google Scholar
• E , W and Wang , XP . 2000 . Numerical methods for the landau--Lifshitz Equation. . SIAM Journal on Numerical Analysis , 38 ( 5 ) : 1647 – 1665 .
   Google Scholar
• Evans , LC . 1998 . Partial Differential Equations , American Mathematical Society .
   Google Scholar
• Guo , B and Hong , M . 1993 . The Landau–Lifshitz equation of the ferromagnetic spin chain and harmonic maps. . Calculus of Variations and Partial Differential Equations , 1 ( 3 ) : 311 – 334 .
   Google Scholar
• Magni , A , Bertotti , G , Mayergoyz , I and Serpico , C . 2002 . Landau–Lifshitz magnetization dynamics and eddy currents in metallic thin films. . Journal of Applied Physics , 91 : 7559 – 7561 .
   Google Scholar
• Magni , A , Bertotti , G , Mayergoyz , I and Serpico , C . 2003 . Landau-Lifshitz-Gilbert dynamics and eddy current effects in metallic thin films. . Journal of Magnetism and Magnetic Materials , 210 : 254 – 255 .
   Google Scholar
• Monk , P . 2003 . Finite Element Methods for Maxwell's Equations , Oxford, , UK : Oxford University Press .
   Google Scholar
• Prohl , A . 2001 . Computational Micromagnetism (Teubner)
   Google Scholar
• Serpico , C and Mayergoyz , I . 2001 . Analysis of eddy currents with Landau–Lifshitz equation as a constitutive relation. . IEEE Transactions on Magnetics , 37 : 3546 – 3549 .
   Google Scholar
• Slodička , M and Cimrák , I . 2003 . Numerical study of ferromagnetic materials. . Applied Numerical Mathematics , 46 : 95 – 111 .
   Google Scholar
• Sun , J . 2005 . Numerical Analysis of Nonlinear Models of Ferromagnetic Materials , University of Delaware . PhD thesis
   Google Scholar
• Sun , J , Collino , F , Monk , P and Wang , L . 2004 . An eddy current and micromagnetism model with applications to disk write heads. . International Journal for Numerical Methods in Engineering , 60 : 1673 – 1697 .
   Google Scholar
• Vacus , O and Monk , P . 2001 . Accurate discretization of non-linear micromagnetic problem. . Computer Methods in Applied Mechanics and Engineering , 190 : 5243 – 5269 .
   Google Scholar
• Visintin , A . 1985 . On Landau-Lifshitz’ equations for ferromagnetism. . Japan Journal of Applied Mathematics , 2 : 69 – 84 .
   Google Scholar
• Wang , XP , Garcia-Cervera , CJ and Weinan , E . 2001 . A Gauss-Seidel projection method for micromagnetics simulations. . Journal of Computational Physics , 171 : 357 – 372 .
   Web of Science ®Google Scholar